Your First Game

Model the most famous game in game theory: the Prisoner's Dilemma.

The Story

Two criminals are arrested and interrogated separately. Each has two choices:

• Cooperate (stay silent) — Don't rat on your partner
• Defect (betray) — Testify against your partner

The outcomes depend on what both players choose:

The Tenet Model

Create a file prisoners_dilemma.tenet:

// Prisoner's Dilemma
// Payoffs represent "years of freedom" (higher = better)

game PrisonersDilemma {
    players Alice, Bob
    strategies Cooperate, Defect
    
    payoff Alice {
        (Cooperate, Cooperate): 3  // Both silent: light sentence
        (Cooperate, Defect): 0     // I'm silent, they rat: worst outcome
        (Defect, Cooperate): 5     // I rat, they're silent: I go free
        (Defect, Defect): 1        // Both rat: moderate sentence
    }
    
    payoff Bob {
        (Cooperate, Cooperate): 3
        (Defect, Cooperate): 0
        (Cooperate, Defect): 5
        (Defect, Defect): 1
    }
}

solve PrisonersDilemma;

Understanding the Payoff Matrix

                    Bob
                C       D
        ┌───────┬───────┐
    C   │ (3,3) │ (0,5) │
Alice   ├───────┼───────┤
    D   │ (5,0) │ (1,1) │
        └───────┴───────┘

Each cell shows (Alice's payoff, Bob's payoff).

The Dilemma

Here's the tragedy:

1. If Alice knows Bob will Cooperate: Alice should Defect (5 > 3)
2. If Alice knows Bob will Defect: Alice should still Defect (1 > 0)

Defect is Alice's dominant strategy — it's better no matter what Bob does.

The same logic applies to Bob. So both players Defect, getting (1, 1).

But wait — if both had Cooperated, they'd get (3, 3)!

This is the dilemma: Individual rationality leads to a collectively worse outcome.

Adding Variables

Make the game parameterized:

var T = 5;  // Temptation to defect
var R = 3;  // Reward for mutual cooperation
var P = 1;  // Punishment for mutual defection
var S = 0;  // Sucker's payoff

// Classic PD requires: T > R > P > S

game ParameterizedPD {
    players P1, P2
    strategies C, D
    
    payoff P1 {
        (C, C): R
        (C, D): S
        (D, C): T
        (D, D): P
    }
    
    payoff P2 {
        (C, C): R
        (D, C): S
        (C, D): T
        (D, D): P
    }
}

solve ParameterizedPD;

Now you can experiment with different payoff values!

What You Learned

• How to define players and strategies
• How to specify payoff matrices
• The concept of dominant strategies
• The Nash equilibrium of the Prisoner's Dilemma

Next Steps

• Model Gallery — Explore more classic games
• Payoff Matrices — Advanced payoff features
• Solving Games — Finding Nash equilibria